Magnetic anisotropy and quantized spin waves in hematite nanoparticles

Abstract

We report on the observation of high-frequency collective magnetic excitations, ប Ϸ 1.1 meV, in hematite ͑␣-Fe 2 O 3 ͒ nanoparticles. The neutron scattering experiments include measurements at temperatures in the range 6-300 K and applied fields up to 7.5 T as well as polarization analysis. We give an explanation for the field-and temperature dependence of the excitations, which are found to have strongly elliptical out-of-plane precession. The frequency of the excitations gives information on the magnetic anisotropy constants in the system. We have in this way determined the temperature dependence of the magnetic anisotropy, which is strongly related to the suppression of the Morin transition in nanoparticles of hematite. Further, the localization of the signal in both energy and momentum transfer brings evidence for finite-size quantization of spin waves in the system.

Magnetic properties of nano-scale hematite, α-Fe2O3, studied by time-of-flight inelastic neutron spectroscopy

“…The same cannot be said of ε − 0 , whose temperature dependence is caused not only by S z , but also from a temperature dependence of κ 1 as shown in Ref. 7.…”

“…Looking carefully at the (003) reflection, it is also possible to observe a small amount of the high frequency mode, Fig. 2(d), as also seen by Klausen et al 7 Slices of the spectra were taken across Q at 1.37 Å −1 and 1.51 Å −1 , with a Q of 0.02 Å −1 and subsequently fitted to the model presented in Eq. (3).…”

“…At all temperatures, a model (as used in previous studies [6][7][8] ) of the incoherent signal (Eq. (2)) was convoluted with the instrument energy resolution to provide the background.…”

“…The values of κ 1 and κ 2 are related to nanoparticle anisotropy constants K 1 and K 2 by K i V = κ i Ns 2 . 7 The magnitude of κ 1 is considered several times larger than the κ 2 term, 6 ignoring the small T-interval where κ 1 changes sign.…”

“…In particular, inelastic neutron scattering has been used to study high-frequency collective magnetic excitations, enabling calculations of magnetic anisotropy constants in the system, and providing a reason for the suppression of the first order magnetic re-orientation Morin transition (expanded upon below). [5][6][7][8] Another interesting topic in dynamics of nanoparticle magnetism is superparamagnetism (SPM), where the magnetization direction spontaneously reverses direction, assisted by temperature in an Arrhenius fashion. This effect is present also for antiferromagnetic hematite, as was shown directly using Mössbauer spectroscopy 9 and by quasi-elastic neutron scattering.…”